Robust Polynomials and Quantum Algorithms

  • Harry Buhrman
  • Ilan Newman
  • Hein Röhrig
  • Ronald de Wolf
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3404)


We define and study the complexity of robust polynomials for Boolean functions and the related fault-tolerant quantum decision trees, where input bits are perturbed by noise. We show that, in contrast to the classical model of Feige et al., every Boolean function can be computed by O(n) quantum queries even in the model with noise. This implies, for instance, the somewhat surprising result that every Boolean function has robust degree bounded by O(n).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Harry Buhrman
    • 1
    • 2
  • Ilan Newman
    • 3
  • Hein Röhrig
    • 4
  • Ronald de Wolf
    • 1
  1. 1.CWIAmsterdamthe Netherlands
  2. 2.ILLCUniversity of Amsterdamthe Netherlands
  3. 3.Dept. of Computer ScienceHaifa UniversityIsrael
  4. 4.Dept. of Computer ScienceUniversity of CalgaryCanada

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